What is the relationship of variance and standard deviation to the mean, median and mode?

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Expert Solution

Explanation:

The variance and standard deviation describe how spread out the data is. If the data all lies close to the mean, then the standard deviation will be small, while if the data is spread out over a large range of values, s will be large. Having outliers will increase the standard deviation.

The relationship between mean median and mode is that they are all measures of central tendencies , that is a measure which shows how closely related are the elements in a distribution while standard deviation on the other hand is a measure of dispersion which shows how scattered the variables are from each other

Mean is the arithmetic average of the data values

Median is the middle value when the data values have been sorted (or the average of the 2 middle values if there are an even number of data values).

Mode is the data value(s) the occur with the greatest frequency.

Variance and Standard Deviation depend upon whether the data is assumed to be the entire population or only a sample from the entire population.

Population Variance (σ^2pop)
is the sum of the squares of the differences between each data value and the mean, divided by the number of data values.

Population Standard Deviation (σpop)
is the square root of σ^2pop

Sample Variance (σ^2smpl)
is the sum of the squares of the differences between each data value and the mean, divided by one less than the number of data values.

Sample Standard Deviation(σsmpl)
is the square root of σ^2smpl

orchestra answered 1 year ago

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